Finite Group Databasebeta

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C23×C42×C92 #72189032

order10368
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 256842399744
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C4×C9

Aliases

abelianC23×C42×C92
multiplicative(ℤ/28120)ˣ, (ℤ/33744)ˣ, (ℤ/39960)ˣ, (ℤ/41040)ˣ, (ℤ/42180)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C32C25×C32
socle, prime radicalC25×C32C22×C32
LCSG ▷ C1
UCSC1 ◁ G

34500 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10368 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C4×C8×C92, C22×C43×C92, C24×C42×C92, …
maximal normal subgroup ofC23×C4×C8×C92, C22×C43×C92, C24×C42×C92, …
maximal quotient ofC23×C4×C8×C92, C22×C43×C92, C24×C42×C92, …
automorphism group ofC5×C8×C19×C37
outer automorphism group ofC5×C8×C19×C37

GAP

Past the SmallGroups library coverage — no SmallGroups id.